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Step 1
Melt 3 tablespoons of the butter in a medium sauce pan over medium-low heat. Add the onion and sauté, stirring frequently, until soft and translucent, about 8 minutes. Do not brown.
Step 2
Add the squash, milk, salt and pepper and bring to a boil. Reduce the heat to medium and slowly add the cornmeal in a thin stream while whisking continuously. (I find it easiest to lightly tap the measuring cup of polenta against the pot so that it sprinkles in.) Reduce the heat to low and simmer, stirring frequently with a whisk, for about 5 minutes or until polenta is smooth and thickened.
Step 3
Remove from the heat and stir in cheese and remaining 2 tablespoons of butter. Serve immediately topped with a bit of butter, more cheese, and herbs (if using). If serving later, place a piece of plastic wrap directly over the polenta to prevent a film from forming and reheat on the stovetop when ready to serve. (You will need to whisk well and add some water or milk to thin it out to the desired consistency when you reheat it.)
Step 4
Note: If you can't find puréed squash, purée it in a food processor or blender. (Mashing it with a fork doesn't work well, as butternut squash is a bit stringy.)